Here are the mistakes in each sentence along with the corrections:

1. **Mistake:** "Having imported from America"
**Correction:** "Having been imported from America"
**Corrected Sentence:** Having been imported from America, the fruit was expensive.

2. **Mistake:** "what"
**Correction:** "that"
**Corrected Sentence:** It is his dishonesty that I dislike the most.

3. **Mistake:** "Although her poor health"
**Correction:** "Due to her poor health" or "Although she has poor health"
**Corrected Sentence:** Due to her poor health, she works twelve hours a day.
(or) Although she has poor health, she works twelve hours a day.

4. **Mistake:** No grammatical mistake, but the sentence could be improved for clarity.
**Correction:** None needed, but can be rephrased for clarity: "Verbal bullying occurs when people spread lies or negative information about you behind your back."
**Corrected Sentence:** Verbal bullying occurs when people keep telling lies or bad things about you behind your back. (optional rephrase for clarity)